We present a simple classical analysis of light interacting with a Fabry-Perot cavity consisting of a fixed (dielectric) front mirror and a vibrating rear mirror. In the adiabatic approximation, the returning light exhibits sideband symmetry, which will go away once the photon lifetime becomes comparable to or longer than the oscillation period of the rear mirror. When the oscillation period is short compared to the cavity photon lifetime, one must approach the problem differently, treating the vibrating mirror as a scatterer which sends a fraction of the incident light into sideband frequencies. With proper detuning, the cavity’s internal radiation pressure could either dampen or amplify the vibrations of the mirror; the former is the physical principle behind opto-mechanical cooling by the back-action of cavity photons.

Combining optical levitation and cavity optomechanics constitutes a promising approach to prepare and control the motional quantum state of massive objects (>10^9 amu). This, in turn, would represent a completely new type of light-matter interface and has, for example, been predicted to enable experimental tests of macrorealistic models or of non-Newtonian gravity at small length scales. Such ideas have triggered significant experimental efforts to realizing such novel systems.
To this end, we have recently successfully demonstrated cavity-cooling of a levitated sub-micron silica particle in a classical regime at a pressure of approximately 1mbar. Access to higher vacuum of approx. 10^-6 mbar has been demonstrated using 3D-feedback cooling in optical tweezers without cavity-coupling.
Here we will illustrate our strategy towards trapping, 3D-cooling and quantum control of nanoparticles in ultra-high vacuum using cavity-based feedback cooling methods and clean particle loading with hollow-core photonic crystal fibers. We will also discuss the current experimental progress both in 3D-cavity cooling and HCPCF-based transport of nanoparticles.
As yet another application of cavity-controlled levitated nanoparticles we will show how to implement a thermodynamic Sterling cycle operating in the underdamped regime. We present optimized protocols with respect to efficiency at maximum power in this little explored regime. We also show that the excellent level of control in our system will allow reproducing all relevant features of such optimized protocols. In a next step, this will enable studies of thermodynamics cycles in a regime where the quantization of the mechanical motion becomes relevant.

We have developed a robust interrogation system using frequency modulation spectroscopy to measure the quantum state-dependent phase shift incurred on an off-resonant optical probe when transmitted by an atomic medium. Recently, our focus has been on extending this technique for the detection of Feshbach resonances in 87Rb atoms. Feshbach resonance is a mechanism which allows the atomic interaction strength to be precisely tuned via an external magnetic field. To access a Feshbach resonance atoms must be independently prepared in certain internal states, during which we utilize programmable optical tweezers to perform precise spatial micro-manipulation of the ensemble in laser “test-tubes.” We use our dispersive probing system to identify the resonant magnetic field value in a sample with a dense “ball” geometry. An important design consideration for such a probing scheme is the three-dimensional mode-matching at the interface between light and the atomic sample when coupled by the dispersive interaction. We discuss challenges which dealing with this new geometry compared to the previously used prolate geometry, and consider the possibility of dipole-dipole interactions in our sample leading to cooperative light scattering processes.

Bessel beam (BB) optical traps have become widely used to confine single and multiple aerosol particles across a broad range of sizes, from a few microns to < 200 nm in radius. The radiation pressure force exerted by the core of a single, zeroth-order BB incident on a particle can be balanced by a counter-propagating gas flow, allowing a single particle to be trapped indefinitely. The pseudo non-diffracting nature of BBs enables particles to be confined over macroscopic distances along the BB core propagation length; the position of the particle along this length can be finely controlled by variation of the BB laser power. This latter property is exploited to optimize the particle position at the center of the TEM00 mode of a high finesse optical cavity, allowing cavity ring-down spectroscopy (CRDS) to be performed on single aerosol particles and their optical extinction cross section, σext, measured. Further, the variation in the light from the illuminating BB elastically scattered by the particle is recorded as a function of scattering angle. Such intensity distributions are fitted to Lorenz-Mie theory to determine the particle radius. The trends in σext with particle radius are modelled using cavity standing wave Mie simulations and a particle’s varying refractive index with changing relative humidity is determined. We demonstrate σext measurements on individual sub-micrometer aerosol particles and determine the lowest limit in particle size that can be probed by this technique. The BB-CRDS method will play a key role in reducing the uncertainty associated with atmospheric aerosol radiative forcing, which remains among the largest uncertainties in climate modelling.

The dynamics of aerosol droplets in a quadruple Bessel beam (QBB) trap and a counter-propagating Bessel beam (CPBB) trap are compared by combining experimental results with simulations of the three-dimensional droplet dynamics. The major focus is on the influence of additional constant and pulsed external forces on the droplet stability and confinement in the two different types of traps. The constant force corresponds to a constant gas flow around the trapped droplet. The pulsed external force is provided by a nanosecond laser. Two types of droplets are studied: Aqueous NaCl droplets which do not absorb at the wavelength of the nanosecond laser and DOP particles which strongly absorb at the wavelength of the nanosecond laser.

We demonstrate the simultaneous measurement of optical trap stiffness and quadrant-cell photodetector (QPD) calibration of optically trapped polystyrene particle in air. The analysis is based on the transient response of particles, confined to an optical trap, subject to a pulsed electrostatic field generated by parallel indium tin oxide (ITO) coated substrates. The resonant natural frequency and damping were directly estimated by fitting the analytical solution of the transient response of an underdamped harmonic oscillator to the measured particle displacement from its equilibrium position. Because, the particle size was estimated independently with video microscopy, this approach allowed us to measure the optical force without ignoring the effects of inertia and temperature changes from absorption.

Aerosol trapping has proven challenging and was only recently demonstrated.1 This was accomplished by utilizing an air chamber designed to have a minimum of turbulence and a laser beam with a minimum of aberration. Individual gold nano-particles with diameters between 80 nm and 200 nm were trapped in air using a 1064 nm laser. The positions visited by the trapped gold nano-particle were quantified using a quadrant photo diode placed in the back focal plane. The time traces were analyzed and the trapping stiffness characterizing gold aerosol trapping determined and compared to aerosol trapping of nanometer sized silica and polystyrene particles. Based on our analysis, we concluded that gold nano-particles trap more strongly in air than similarly sized polystyrene and silica particles. We found that, in a certain power range, the trapping strength of polystyrene particles is linearly decreasing with increasing laser power.

Optical trapping of light-absorbing particles in a gaseous environment is governed by a laser-induced photophoretic force, which can be orders of magnitude stronger than the force of radiation pressure induced by the same light intensity. In spite of many experimental studies, the exact theoretical background underlying the photophoretic force and the prediction of its influence on the particle motion is still in its infancy. Here, we report the results of a quantitative analysis of the photophoretic force and the stiffness of trapping achieved by levitating graphite and carbon-coated glass shells of calibrated sizes in an upright diverging hollow-core vortex beam, which we refer to as an ‘optical funnel’. The measurements of forces were conducted in air at various gas pressures in the range from 5 mbar to 2 bar. The results of these measurements lay the foundation for developing a touch-free optical system for precisely positioning sub-micrometer bioparticles at the focal spot of an x-ray free electron laser, which would significantly enhance the efficiency of studying nanoscale morphology of proteins and biomolecules in femtosecond coherent diffractive imaging experiments.

Continuum electrodynamics is an axiomatic formal theory based on the macroscopic Maxwell equations and the constitutive relations. We apply the formal theory to a thermodynamically closed system consisting of an antireection coated block of dielectric situated in free-space and illuminated by a quasimonochromatic field. We show that valid theorems of the formal theory are proven false by relativity and by conservation laws. Then the axioms of the formal theory are proven false at a fundamental level of mathematical logic. We derive a new formal theory of continuum electrodynamics for macroscopic electric and magnetic fields in a four-dimensional at non-Minkowski material spacetime in which the speed of light is c/n.

We present examples of simple electromagnetic systems in which energy, linear momentum, and angular momentum exhibit interesting behavior. The systems are sufficiently simple to allow exact solutions of Maxwell’s equations in conjunction with the electrodynamic laws of force, torque, energy, and momentum. In all the cases examined, conservation of energy and momentum is confirmed.

Modeling the dynamics of optical manipulation experiments relies upon a precise mathematical representation of electromagnetic fields and the interpretation of optical momentum and stresses in materials. However, the momentum of light within media has been an issue of debate over the past century. Multiple energy-momentum models have been advanced, each, under certain conditions, agreeing with experimental observation and mathematically consistent with classical electromagnetism. The modern view is that the various formulations of electrodynamics represent different divisions of the total energy-momentum tensor, with the separation of field and matter being ambiguous. Recently, a proposed view of photon momentum identified two leading forms as the kinetic and canonical momenta. The Abraham momentum is responsible for the overall center-of-mass translation of a material, while the Minkowski momentum is responsible for translations with respect to the surrounding medium. However, the Abraham momentum corresponds to multiple, unique electromagnetic energy-momentum tensors that attempt to separate field from material responses (e.g. Abraham, Chu, and Einstein-Laub). However, only the form of the kinetic momentum density has been revealed, while the formulation that uniquely separates the kinetic stress tensor has remained ambiguous. In this correspondence, multiple formulations are considered within the framework of relativistic electrodynamics. We apply various mathematical techniques to identify the kinetic subsystem of electrodynamics. While optical manipulation is usually modeled using a stationary medium approximation, the lessons from relativistic electrodynamics reveal a specific distribution of electromagnetic stress in media. The physics of optical and static manipulation of dielectric particles are described within this framework.

The laser-induced intermolecular force that exists between two or more particles subjected to a moderately intense laser beam is termed ‘optical binding’. Completely distinct from the single-particle forces that give rise to optical trapping, the phenomenon of optical binding is a manifestation of the coupling between optically induced dipole moments in neutral particles. In conjunction with optical trapping, the optomechanical forces in optical binding afford means for the manipulation and fabrication of optically bound matter. The Casimir-Polder potential that is intrinsic to all matter can be overridden by the optical binding force in cases where the laser beam is of sufficient intensity. Chiral discrimination can arise when the laser input has a circular polarization, if the particles are themselves chiral. Then, it emerges that the interaction between particles with a particular handedness is responsive to the left- or right-handedness of the light. The present analysis, which expands upon previous studies of chiral discrimination in optical binding, identifies a novel mechanism that others have previously overlooked, signifying that the discriminatory effect is much more prominent than originally thought. The new theory leads to results for freely-tumbling chiral particles subjected to circularly polarized light. Rigorous conditions are established for the energy shifts to be non-zero and display discriminatory effects with respect to the handedness of the incident beam. Detailed calculations indicate that the energy shift is larger than those previously reported by three orders of magnitude.

We treat the light-matter interaction due to radiation pressure in one dimension using the fundamental, nonrelativistic conservation principles of energy and momentum. Additionally, we assume that the center of mass-energy maintains the same uniform motion if the interaction takes place or not. Since we handle solids as elastic objects, the results are consistent with the principle of causality and agree with recent experimental observations. We analyze the problem of reflection of a light pulse from a fully-reflective mirror and show that its reflection gives rise to an elastic wave with a measurable amplitude and a correct Doppler shift of the reflected pulse. We also analyze the problem of light pulse transmission into an anti-reflection coated, non-dispersive and lossless dielectric, where an elastic wave may as well be accompanied by a mechanical wave escorting the light pulse. We show that the Balazs rigid box thought experiment can be also realized in elastic dielectrics where some of the energy of the incident light is transferred to the wave motion. It follows from our approach that the electromagnetic momentum of the light pulse in the dielectric acquires Abraham’s form only when a single type of the mechanical waves accompanies the interaction.

Optodynamics treats optical manipulation as a superposition of time-developing wave motion induced by a light-matter interaction. When an opaque solid object is manipulated by a pulse of light, various types of mechanical waves are launched from the illuminated surface: ablation-induced waves (AIWs) resulting from material recoil, thermoelastic waves (TEWs), and the light-pressure-induced waves (LIWs) emanating exclusively due to radiation pressure. The manipulated object’s boundaries experience staircase-like displacements with discrete steps caused either by AIWs or LIWs each time these waves are reflected from the interfaces. On the contrary, TEWs cannot translate the center of mass of the manipulated object, but their presence can be inferred from the transient, bi-polar displacements around the equilibrium position.

Traumatic brain injury (TBI) represents a major treatment challenge in both civilian and military medicine; on the cellular level, its mechanisms are poorly understood. As a method to study the dysfunctional repair mechanisms following injury, laser induced shock waves (LIS) are a useful way to create highly precise, well characterized mechanical forces. We present a simple model for TBI using laser induced shock waves as a model for damage. Our objective is to develop an understanding of the processes responsible for neuronal death, the ways in which we can manipulate these processes to improve cell survival and repair, and the importance of these processes at different levels of biological organization. The physics of shock wave creation has been modeled and can be used to calculate forces acting on individual neurons. By ensuring that the impulse is in the same regime as that occurring in practical TBI, the LIS model can ensure that in vitro conditions and damage are similar to those experienced in TBI. This model will allow for the study of the biochemical response of neurons to mechanical stresses, and can be combined with microfluidic systems for cell growth in order to better isolate areas of damage.

We show that microscopic explosions (cavitation bubbles) can be generated periodically in an optical tweezer. An absorbing microparticle is attracted to the trapping beam waist where it eventually superheats a small volume of liquid resulting in a cavitation bubble that impulsively pushes the particle close to the starting position where the cycle restarts. The bubbles expand and collapse in a timescale on the order of one microsecond and are detected with a high speed video recorder and a fast photodiode. We also present preliminary results on the interaction between two microparticles generating cavitation bubbles in the same optical trap.

We have developed a technique of generating a micro-bubble inside an optical trap by using a material (Mo-based Soft Oxometalate (SOM) compound) that absorbs at the trapping laser wavelength. A high concentration aqueous dispersion of the SOMs is taken in a sample chamber, and the trapping laser is focused on SOMs adsorbed on one of the surfaces of the chamber, so as to create a hot spot due to which a microbubble is nucleated. Due to the temperature gradient on the bubble, a surface tension gradient results, which leads to Marangoni type flows around the bubble. The resultant Marangoni ow around the bubble causes self-assembly of material at its base, which undergoes a phase transition into a crystalline state when the laser spot is translated causing the bubble to follow due to convective effects.1 We have used this technique to pattern materials ranging from dyes to carbon nano-tubes to conducting polymers which co-assemble in a mixture with the SOMs. The method is rather universal and has been used to develop catalytic chips2 and solution processed printable electronics. The flow generated by the bubbles can be studied by mapping the trajectories of probe particles in the vicinity of the bubble. We show interesting self-assembly of the particles on the bubble surface, as well as manipulation of trajectories of the particles by multiple bubbles. The bubble can also be used to capture, transport, and release particles in a perfectly controlled manner.

Region specific DNA breaks can be created in single cells using laser light that damages DNA but does not directly generate reactive oxygen species (ROS). We have examined the cellular response to directly generated DNA breaks in single cells. Using a combination of ROS specific dyes and oxidase inhibitors we have found that the oxidase and chromatin remodeling protein Lysine demethylase I (LSD1) generates detectable ROS as a byproduct of its chromatin remodeling activity during the initial DNA damage response. ROS is produced at detectable amounts primarily within the first 3 minutes post irradiation. LSD1 activity has been previously associated with transcriptional regulation therefore these findings have implications for regulation of gene expression following DNA damage particularly in cells with altered redox states.

Biological research requires high-speed and low-damage imaging techniques for live specimens in areas such as development study in embryos. Light sheet microscopy provides fast imaging speed whilst keeps the photo-damage and photo-blenching to minimum. Conventional sample embedding methods in light sheet imaging involves using agent such as agarose which potentially affects the behavior and the develop pattern of the specimens. Here we demonstrate integrating dual-beam trapping method into light sheet imaging system to confine and translate the specimen whilst light sheet images are taken. Tobacco plant cells as well as Spirobranchus lamarcki larva were trapped solely with optical force and sectional images were acquired. This now approach has the potential to extend the applications of light sheet imaging significantly.

Optical diffraction tomography (ODT) is a tomographic technique that can be used to measure the three-dimensional (3D) refractive index distribution within living cells without the requirement of any marker. In principle, ODT can be regarded as a generalization of optical projection tomography which is equivalent to computerized tomography (CT). Both optical tomographic techniques require projection-phase images of cells measured at multiple angles. However, the reconstruction of the 3D refractive index distribution post-measurement differs for the two techniques. It is known that ODT yields better results than projection tomography, because it takes into account diffraction of the imaging light due to the refractive index structure of the sample. Here, we apply ODT to biological cells in a microfluidic chip which combines optical trapping and microfluidic flow to achieve an optofluidic single-cell rotation. In particular, we address the problem that arises when the trapped cell is not rotating about an axis perpendicular to the imaging plane, but is instead arbitrarily tilted. In this paper we show that the 3D reconstruction can be improved by taking into account such a tilted rotational axis in the reconstruction process.

Interferometry can completely redirect light, providing the potential for exceptionally strong and controllable optical forces. When a beamsplitter combines two fields, the output power is directed via the relative phase between the incident fields. Since the phase changes with beamsplitter displacement, the interference force can be used to stably trap; with displacements as small as (λ/4n) able to completely redirect the light. The resulting change in optical momentum causes an opposing optical force. However, optical forces are most useful for trapping and manipulating small scattering particles. Optical scattering is not generally thought to allow efficient interference; essentially, it appears that small particles cannot act as beamsplitters. As such, optical traps have relied upon much weaker deflection-based forces.
Here we show that efficient interference can be achieved by appropriately structuring the incident light. This relies on Mie scattering fringes to combine light which is incident from different incident angles. This results in a force, which we call the structured interference force, which offers order-of-magnitude higher trap stiffness over the usual Gaussian trap. We demonstrate structured interference force trapping (SIFT) of 10μm diameter silica spheres with a stiffness 20.1 times higher than is possible using Gaussian traps, while also increasing the measurement signal-to-noise ratio by two orders of magnitude. This is demonstrated using only phase control of the incident light, making the technique directly compatible with most existing holographic optical traps. These results are highly relevant to many applications, including cellular manipulation, fluid dynamics, micro-robotics, and tests of fundamental physics.

Optical tweezers use highly focussed beams to trap microscopic particles in three dimensions. It is possible to carry out quantitative force measurements, on the order of piconewtons, if calibration of the system is done first. This requires finding the optical force for a given trapping power and position in the trap. Two tools commonly used for calibration are the camera and position-sensitive detector (PSD). Both are commonly used to track trapped particles, but they give complementary information. The camera gives the position of the particle. The PSD measures the defection of the beam, which is the force exerted on the particle. Since these data are obtained on different instruments, usually at vastly different rates, there is difficulty in synchronising the force and position data. Here we look at a force calibration method, without synchronising the data, by mapping force and position measurements. If the force-position relation is monotonic, then the median of the force distribution corresponds to the median of the position distribution; in general, the nth percentile of one corresponds to the (100-n)th percentile of the other. This intuitively works for traps whose force-position relations are monotonic, which includes Hookean traps like a single round symmetric trap. We discuss the limits at which this method can be applied to non-Hookean trapping arrangements, such as independent or coherent double-well traps.

Optical traps allow for the precise application and measurement of pico-Newton forces in a wide variety of situations, and are particularly well suited for biophysical measurements of motor proteins and cells. Nearly all experiments exploit the linear regime of the optical trap, where force and displacement are related by a simple spring constant that does not depend on the trapped object’s position. This typically limits the useful force range to < 100 pN for high-NA objective lenses and reasonable laser powers. Several biological studies require larger forces, which are not accessible in the linear regime of the trap. The best means to extend the maximum force is to make use of the entire nonlinear range; however, current techniques for calibrating the full nonlinear regime are limited. Here we report a new method for calibrating the nonlinear trap region that uses the fluctuations in the position of a trapped object when it is displaced from the center of a single gradient optical trap by controlled flow. From the position fluctuations, we measure the local trap stiffness, in both the linear and non-linear regimes. This approach requires only knowledge of the system temperature, and is especially useful for measurements involving trapped objects of unknown size, or objects in a fluid of unknown viscosity.

The potential of photonic force microscopy (PFM) to directly probe the field of the Bloch surface wave (BSW) in a one-dimensional photonic crystal is considered. Optical forces acting on a dielectric microparticle in the evanescent field of the BSW are estimated in the dipole approximation and calculated by finite-difference time-domain (FDTD) analysis. Technical details of the PFM measurements are described.

We demonstrate optical trapping of a periodic array of closely spaced gold nanoparticles. To achieve the experimental result, we considered competition between optical gradient forces and strong interparticle interactions. We achieve control of the gradient forces using a photonic-crystal template designed to create a periodic optical trapping potential. We modeled the interparticle interactions using a kinetic Monte Carlo approach. The results predict the formation of different particle superstructures (such as chains or filled-in arrays) depending on lattice constant and symmetry. Using the model prediction, we designed and demonstrated a template that allows trapping of a regular periodic array.

The use of optical micro- and nanofibers has become commonplace in the areas of atom trapping using neutral atoms and, perhaps more relevantly, the optical trapping and propulsion of micro- and nanoscale particles. It has been shown that such fibers can be used to manipulate and trap silica and polystyrene particles in the 1-3 µm range using either the fundamental or higher order modes of the fibers, with the propulsion of smaller particle sizes also possible through the use of metallic and/or high index materials. We previously proposed using a focused ion beam nanostructured tapered optical fiber for improved atom trapping geometries; here, we present the details of how these nanostructured optical fibers can be used as a platform for submicron particle trapping. The optical fibers are tapered to approximately 1.2 µm waist diameters, using a custom-built, heat-and-pull fiber rig prior to processing using a focused ion beam. Slots of approximately 300 nm in width and 10-20 µm in length are milled clean though the waist regions of the tapered optical fibers. High fiber transmissions (> 80%) over a broad range of wavelengths (700-1100 nm) are observed. We present simulation results for the trapping of submicron particles and experimental results on the trapping of 200 nm particles. This work demonstrates even further the functionality of optical micro- and nanofibers as trapping devices across a range of regimes.

Sensitive flowmeter with a large dynamic range is highly desirable for microfluidic applications. We developed an optofluidic flow rate sensor, with a dynamic range of about 3 orders of magnitude, based on the optical manipulation of a microparticle by a single mode fiber (SMF) with a flat endface. A single polystyrene microsphere was trapped on the optical axis by the 980 nm laser emitting from SMF and the force balance between the optical force and flow force was used for sensing. The manipulation distance was detected as a function of the flow rate. The measurement range of the flow rate can cover 20 - 22000 nL/min with a laser power of 11.4 mW to 146.3 mW. The maximum manipulation length is about 715 μm. The experimental results indicate that the sensor has a good repeatability for the flow rate measurement.

Bessel beams are important for applications in optical trapping because they have non-diffracting and self-reconstructing properties. We fabricated a fiber device to generate a Bessel-like beam that is significantly more compact than a conventional bulk-optic Bessel beam generation system. Micro-scale dielectric particles in water are trapped and transported along the optical route formed by this Bessel-like beam. By controlling the speed and angular motion of the particles, we have demonstrated optically induced circulation of particles along triangular routes. This technique is applicable to the control of motion of living cells in a microscopic environment.

Optical micro- and nanofibers have attracted great interest due to their potential for trapping and manipulating micronsized particles in the evanescent field that extends from their surface. To date, most particle manipulation research has been limited to fundamental mode propagation within the ultrathin fiber. In this work, we study propulsion of polystyrene particles under the influence of the evanescent field from the first order guided modes and compare it to the fundamental mode case. Speeds of single and double particles are compared, and the optical binding effect between particles is analyzed. The dependence of the particles’ speeds on their diameter is studied for 1 μm, 3 μm, and 5 μm diameter polystyrene particles using the higher order modes of the fibers. Furthermore, we also study the material dependence of particle propulsion speeds.

Stochastic thermodynamics [1,2] is a recently developed framework to deal with the thermodynamics at the microscope, where thermal fluctuations strongly influence their behaviour. Typical such systems are colloids and biomolecules or cells. These thermal fluctuations do not only lead to Brownian motion, but to a continuous and unavoidable heat exchange between the suspending medium and the particles, leading to a very interesting phenomenology. In order to explore such phenomenology and to test theoretical results obtained from stochastic thermodynamics, we developed an “experimental simulator” of thermodynamic devices in the microscale with an optically trapped bead that is subject to an external noise that mimics a controllable thermal bath. The noise is applied by means of electric fields acting on the charge of the trapped particle.
In this talk, I will present some of the results we obtained with this simulator, demonstrating excellent control over the effective temperature of the system and a control parameter. This allows us to perform a variety of equilibrium and non-equilibrium thermodynamic processes [3-5]. In particular, we were able to realize microadiabatic processes, where no heat is exchanged on average between the particle and the medium [6]. This achievement allowed us to implement a Carnot microengine as a concatenation of isothermal and adiabatic processes [7], whose theoretical study is playing a key role in the foundations of stochastic thermodynamics.
References
[1] K Sekimoto; Lecture Notes in Physics (Springer, Berlin, 2010), Vol. 799.
[2] U Seifert; Rep. Prog. Phys. 75 (2012) 126001
[3] IA Martínez, E Roldan, JMR Parrondo, D Petrov; Phys. Rev. E 87 (2013) 032159
[4] É Roldán, IA Martínez, L Dinis, RA Rica; Appl. Phys. Lett. 104 (2014) 234103
[5] P Mestres, IA Martinez, A Ortiz-Ambriz, RA Rica, E Roldan; Phys. Rev. E 90 (2014) 032116
[6] IA Martínez, E Roldan, L Dinis, D Petrov, RA Rica; Phys. Rev. Lett. (2015) In press
[7] IA Martinez, E Roldan, L Dinis, D Petrov, JMR Parrondo, RA Rica; (2015) arXiv preprint: 1412.1282

With the use of optical traps it is possible to confine assemblies of colloidal particles in two-dimensional and quasi-one-dimensional arrays. Here we examine how colloidal particles rearrange in a quasi-one-dimensional trap with a time dependent confining potential. The particle motion occurs both through slow elastic uniaxial distortions as well as through abrupt large-scale two-dimensional avalanches associated with plastic rearrangements. During the avalanches the particle velocity distributions extend over a broad range and can be fit to a power law consistent with other studies of plastic events mediated by dislocations.

Because of their unique characteristics, colloids have been used to investigate the fundamental physics of soft materials including both equilibrium phase behavior and kinetic processes. Unlike atoms, colloidal sizes can be conveniently tailored and are typically large enough to be probed individually with interaction strengths and effective ranges that can be modulated over several orders of magnitude. Despite these significant advantages, only relatively simple colloidal models such as spheres have been created; such systems in turn assemble into crystals of fairly limited symmetry, precluding the study of problems associated with complex structure. To push towards the synthesis of more complicated colloidal molecules, we use combined applied magnetic and anisotropic optical fields to fabricate colloidal chains. By integrating these induced forces within microfluidic channels and in flow, we grow colloidal chains one particle at one time, mimicking step-growth polymerization. The key advantage of this method is the ability to precisely control chain length and sequence, both essential for studies of self-assembly. In this, chain length is determined by a balance between the hydrodynamic shear stress, applied magnetic field, and the optical forces applied. Once a desired chain length is achieved, we fix the assembly in situ via the use of thiol-functionalized magnetic beads and a functionalized polyethylene glycol crosslinker. With the ability to perform directed assembly and irreversible fixation in flow, a route to the high-throughput synthesis of colloidal molecules can be achieved.

The ability to precisely manipulate micro- and nano-scale objects has been a major driver in the progression of nanotechnologies. In this proceedings we describe a form of micro-manipulation in which the position of a target object can be controlled via locally generated fluid flow, created by the motion of nearby optically trapped objects. The ability to do this relies on a simple principle: when an object is moved through a fluid, it displaces the surrounding fluid in a predictable manner, resulting in controllable hydrodynamic forces exerted on adjacent objects. Therefore, by moving optically trapped actuators using feedback in response to a target object's current position, the flow-field at the target can be dynamically controlled. Here we investigate the performance of such a system using stochastic Brownian dynamics simulations, which are based on numerical integration of the Langevin equation describing the evolution of the system, using the Rotne-Praga approximation to capture hydrodynamic interactions. We show that optically controlled hydrodynamic micro-manipulation has the potential to hold target objects in place, move them along prescribed trajectories, and damp their Brownian motion, using the indirect forces of the surrounding water alone.

Hydrodynamic coupling is thought to play a role in the coordinated beating of cilia and flagella, and may inform the future design of artificial swimmers and pumps. In this study, optical tweezers are used to investigate the hydrodynamic coupling between a pair of driven oscillators. The theoretical model of Lenz and Ryskin [P. Lenz and A. Ryskin, Phys. Biol. 3, 285{294 (2006)] is experimentally recreated, in which each oscillator consists of a sphere driven in a circular trajectory. The optical trap position is maintained ahead of the sphere to provide a tangential driving force. The trap is also moved radially to harmonically constrain the sphere to the circular trajectory. Analytically, it has been shown that two oscillators of this type are able to synchronise or phase-lock under certain conditions. We explore the interplay between synchronisation mechanisms and find good agreement between experiment, theory and Brownian dynamics simulations.

Boundary walls have a strong influence on the drag force on optically trapped object near surface. Faxen’s correction has shown how a flat surface modifies the hydrodynamic drag. However, to date, the effect of curved walls at microscopic scale on both translational and rotational movement of micro-objects has not been studied. Here we describe our experiments which aim to study the drag force on optically trapped particles moving near walls with different curvatures.
The curved walls were made using 3D laser nano-printing (Nanoscribe), and optical tweezers were used to trap micro-objects near the walls. The translational and rotational motion of the optically trapped particle is related to the drag coefficients. By monitoring the change in the motion of particle, we determined the increase in drag force for particles translating or rotating at different distances from surfaces with different curvatures.
These results are essential for calibrating the drag force on particles, and thus enable accurate rheology at the micron-scale. This opens the potential for microrheology under different conditions, such as within microdevices, biological cells and studies of biological processes

The potential use of optical forces in microfluidic environment enables highly selective bio-particle manipulation. Manipulation could be accomplished via trapping or pushing a particle due to optical field. Empirical determination of optical force is often needed to ensure efficient operation of manipulation. The external force applied to a trapped particle in a microfluidic channel is a combination of optical and drag forces. The optical force can be found by measuring the particle velocity for a certain laser power level and a multiplicative correction factor is applied for the proximity of the particle to the channel surface. This method is not accurate especially for small microfluidic geometries where the particle size is in Mie regime and is comparable to channel cross section. In this work, we propose to use Boundary Element Method (BEM) to simulate fluid flow within the micro-channel with the presence of the particle to predict drag force. Pushing experiments were performed in a dual-beam optical trap and particle’s position information was extracted. The drag force acting on the particle was then obtained using BEM and other analytical expressions, and was compared to the calculated optical force. BEM was able to predict the behavior of the optical force due to the inclusion of all the channel walls.

Larger golden nanoparticles grow into several preferred forms. Some of those may be easily approximated by ellipsoids. In this paper we examine the rotational dynamics of spheroidal particles in an optical trap comprising counter-propagating Gaussian beams of opposing helicity. Isolated spheroids undergo continuous rotation with frequencies determined by their size and aspect ratio. We study the rotational frequencies and stability of these golden nano-particles theoretically by the means of T-Matrix.

We report on the nonlinear effects of light propagation through a fluorescent nanocolloid, where self-collimated beams are formed. The medium is constituted by a bidisperse suspension of fluorescent and nonfluorescent nanospheres of similar diameters (60nm and 62nm, respectively) in distilled water. A CW laser beam (532 nm wavelength) was focused into the nano-suspension. The threshold power and focusing conditions to create a self-collimated beam are analyzed as a function of the incident power, and a hysteresis effect is observed for the size of the output beam when the power is increasing and decreasing. We also discuss other effects associated to the presence of the fluorescent nanospheres.

There has been tremendous growth in the field of active matter, where the individual particles that comprise the system are self-driven. Examples of this class of system include biological systems such as swimming bacteria and crawling cells. More recently, non-biological swimmers have been created using colloidal Janus particles that undergo chemical reactions on one side to produce self-propulsion. These active matter systems exhibit a wide variety of behaviors that are absent in systems undergoing purely thermal fluctuations, such as transitions from uniform liquids to clusters or living crystals, pushing objects around, ratchet effects, and phase separation in mixtures of active and passive particles. Here we examine the collective effects of active matter disks in the presence of static or dynamic substrates. For colloids, such substrates could be created optically in the form of periodic, random, or quasiperiodic patterns. For thermal particles, increasing the temperature generally increases the diffusion or mobility of the particles when they move over a random or periodic substrates. We find that when the particles are active, increasing the activity can increase the mobility for smaller run lengths but decrease the mobility at large run lengths. Additionally we find that at large run lengths on a structured substrate, a variety of novel active crystalline states can form such as stripes, squares and triangular patterns.

Particles undergoing a stochastic motion within a disordered medium is a ubiquitous physical and biological phenomenon. Examples can be given from organelles as molecular machines of cells performing physical tasks in a populated cytoplasm to human mobility in patchy environment at larger scales. Our recent results showed that it is possible to use the disordered landscape generated by speckle light fields to perform advanced manipulation tasks at the microscale. Here, we use speckle light fields to study the anomalous diffusion of micron size silica particles (5 μm) in the presence of active microswimmers. The microswimmers we used in the experiments are motile bacteria, Escherichia coli (E.coli). They constitute an active background constantly agitating passive silica particles within complex optical potentials. The speckle fields are generated by mode mixing inside a multimode optical fiber where a small amount of incident laser power (maximum power = 12 μW/μm2) is needed to obtain an effective random landscape pattern for the purpose of optical manipulation. We experimentally show how complex potentials contribute to the anomalous diffusion of silica particles undergoing collisions with swimming bacteria. We observed an enhanced diffusion of particles interacting with the active bath of E.coli inside speckle light fields: this effect can be tuned and controlled by varying the intensity and the statistical properties of the speckle pattern. Potentially, these results could be of interest for many technological applications, such as the manipulation of microparticles inside optically disordered media of biological interests.

Living cells are a non-equilibrium mechanical system, largely because intracellular molecular motors consume chemical energy to generate forces that reorganize and maintain cytoskeletal functions. Persistently under tension, the network of cytoskeletal proteins exhibits a nonlinear mechanical behavior where the network stiffness increases with intracellular tension. We examined the nonlinear mechanical properties of living cells by characterizing the differential stiffness of the cytoskeletal network for HeLa cells under different intracellular tensions. Combining optical tweezer-based active and passive microrheology methods, we measured non-thermal fluctuating forces and found them to be much larger than the thermal fluctuating force. From the variations of differential stiffness caused by the fluctuating non-thermal force for cells under different tension, we obtained a master curve describing the differential stiffness as a function of the intracellular tension. Varying the intracellular tension by treating cells with drugs that alter motor protein activities we found the differential stiffness follows the same master curve that describes intracellular stiffness as a function of intracellular tension. This observation suggests that cells can regulate their mechanical properties by adjusting intracellular tension.

Fluorescence correlation spectroscopy (FCS) is an optical technique in which the fluctuations in fluorescence intensity are quantified. The time correlation function gives insight into the dynamics of the molecule in its environment: typically the diffusion coefficient in a dilute solution is measured, but the technique has been expanded to uses in more complex environments, including living cells. In these environments photobleaching and dye-dissociation can substantially introduce artifacts in the FCS data. We present a technique to correct for the artifacts introduced by photobleaching and study dye dissociation in DNA solutions.

We present cumulative perturbation effects of femtosecond laser pulses on an optical tweezer. Our experiments involve a dual wavelength high repetition rate femtosecond laser, one at the non-heating wavelength of 780 nm while the other at 1560 nm to cause heating in the trapped volume under low power (100-800 μW) conditions. The 1560 nm high repetition rate laser acts as a resonant excitation source for the vibrational combination band of the hydroxyl group (OH) of water, which helps create the local heating effortlessly within the trapping volume. With such an experimental system, we are the first to observe direct effect of temperature on the corner frequency deduced from power spectrum. We can, thus, control and measure temperature precisely at the optical trap. This observation has lead us to calculate viscosity as well as temperature in the vicinity of the trapping zone. These experimental results also support the well-known fact that the nature of Brownian motion is the response of the optically trapped bead from the temperature change of surroundings. Temperature rise near the trapping zone can significantly change the viscosity of the medium. However, we notice that though the temperature and viscosity are changing as per our corner frequency calculations, the trap stiffness remains the same throughout our experiments within the temperature range of about 20 K.

We investigate holographic optical tweezing combined with step-and-repeat maskless projection micro-stereolithography for fine control of 3D positioning of living cells within a 3D microstructured hydrogel grid. Samples were fabricated using three different cell lines; PC12, NT2/D1 and iPSC. PC12 cells are a rat cell line capable of differentiation into neuron-like cells NT2/D1 cells are a human cell line that exhibit biochemical and developmental properties similar to that of an early embryo and when exposed to retinoic acid the cells differentiate into human neurons useful for studies of human neurological disease. Finally induced pluripotent stem cells (iPSC) were utilized with the goal of future studies of neural networks fabricated from human iPSC derived neurons. Cells are positioned in the monomer solution with holographic optical tweezers at 1064 nm and then are encapsulated by photopolymerization of polyethylene glycol (PEG) hydrogels formed by thiol-ene photo-click chemistry via projection of a 512x512 spatial light modulator (SLM) illuminated at 405 nm. Fabricated samples are incubated in differentiation media such that cells cease to divide and begin to form axons or axon-like structures. By controlling the position of the cells within the encapsulating hydrogel structure the formation of the neural circuits is controlled. The samples fabricated with this system are a useful model for future studies of neural circuit formation, neurological disease, cellular communication, plasticity, and repair mechanisms.

The spatial connectivity of neural circuits and the various activity patterns they exert is what forms the brain function. How these patterns link to a certain perception or a behavior is a key question in neuroscience. Recording the activity of neural circuits while manipulating arbitrary neurons leads to answering this question. That is why acquiring a fast and reliable method of stimulation and imaging a population of neurons at a single cell resolution is of great importance. Owing to the recent advancements in calcium imaging and optogenetics, tens to hundreds of neurons in a living system can be imaged and manipulated optically. We describe the adaptation of a multi-point optical method that can be used to address the specific challenges faced in the in-vivo study of neuronal networks in the cerebral cortex. One specific challenge in the cerebral cortex is that the information flows perpendicular to the surface. Therefore, addressing multiple points in a three dimensional space simultaneously is of great interest. Using a liquid crystal spatial light modulator, the wavefront of the input laser beam is modified to produce multiple focal points at different depths of the sample for true multipoint two-photon excitation.

This talk will present a nanoaperture tweezer approach to measure the acoustic spectra of viruses and single proteins. The approach, termed extraordinary optical Raman (EAR), shows promise for uncovering the structure and mechanical properties of nanoparticles as well as the effects of their interactions.

We study the optical properties of hybrid gold nanodisk and nanohole arrays and present experimental evidence of nanoparticle trapping using these devices. The fabrication procedure using electron beam lithography (EBL) is also discussed. This hybrid design exhibits a splitting of the resonance modes (low and high energy modes) due to the coupling of the electromagnetic interaction between nanohole and nanodisk plasmons. The devices demonstrate high plasmon resonance tunabilities from the visible to the near-infrared region (NIR) by varying the dimensions of the features of this design. This enhancement in the NIR is highly desirable for the purposes of biological sample manipulation where photo damage should be low. Additionally, these devices consist of grooves connecting the hybrid structures to each other. These regions provide further enhancement of the local electric fields and play the role of the trapping sites. We demonstrate multiple dielectric nanoparticle trapping in these grooves while the devices are excited by evanescent fields via the Kretschmann configuration. The results provide good evidence of the potential of this design to be used for the manipulation of biological samples with sub-diffraction limit sizes.

Gold nanoparticles (GNP) have wide applications ranging from nanoscale heating to cancer therapy and biological sensing. Optical trapping of GNPs as small as 18 nm has been successfully achieved with laser power as high as 855 mW, but such high powers can damage trapped particles (particularly biological systems) as well heat the fluid, thereby destabilizing the trap.
In this article, we show that counter propagating beams (CPB) can successfully trap GNP with laser powers reduced by a factor of 50 compared to that with a single beam. The trapping position of a GNP inside a counter-propagating trap can be easily modulated by either changing the relative power or position of the two beams. Furthermore, we find that under our conditions while a single-beam most stably traps a single particle, the counter-propagating beam can more easily trap multiple particles. This (CPB) trap is compatible with the feedback control system we recently demonstrated to increase the trapping lifetimes of nanoparticles by more than an order of magnitude. Thus, we believe that the future development of advanced trapping techniques combining counter-propagating traps together with control systems should significantly extend the capabilities of optical manipulation of nanoparticles for prototyping and testing 3D nanodevices and bio-sensing.

When a nanorod of typically d=100's nm diameter and h=1-3 micrometers length trapped in the optical tweezers, its orientation is along the trapping beam axis for h/d > 2 and is normal to beam axis for h/d < 2. We report the preliminary experimental observation that some anisotropic single crystal nanorod was stably trapped at a tiled angle to the beam axis. We explain the observation with the T-matrix calculation. In the anisotropic media, as the divergence of is non zero, the conventional vector spherical wave functions (VSWFs) do not individually satisfy the anisotropic vector wave equation. Some new bases, such as the modified VSWFS and qVSWF, have been proposed. Notice that the anisotropic nanorod is floating in the aquatic isotropic medium, we make the VSWF expansions of the incident and scattered fields in terms of, and the VSWF expansion of internal field in the anisotropic nanorod in terms of. Both expansions are therefore legitimate. The boundary condition was chosen as for the normal components of. The internal field is represented as a sum of a set of compoment VSWF expansions to gave better description with more expansion coefficients and to help the convergence of the T-matrix solver. Our calculation showed that when the optical axes of an anisotropic nanorod are not aligned to the nanorod axis, the nanorod may be trapped at a tilted angle position where the lateral torque is zero and its derivative is negative.

Asymmetric particles, such as biological cells, often experience torque under optical tweezers. The cause is believed to be either birefringence or unbalanced scattering forces. The estimate of torque relies on the accurate measurement of rotational motion. Here we present a new technique to quantify the asymmetry of trapped particles relying upon the cross coupling between rotational and translational Brownian motion. We observe that RBC does indeed show cross coupling indicating asymmetry of the shape. Further we also show by polarimetry that the retardance of the RBC is not sufficient to make it rotate since the scattering torque is much higher.

It is well known that a rigid pendulum with minimal friction will occupy a stable equilibrium position vertically upwards when its suspension point is oscillated at high frequency. The phenomenon of the inverted pendulum was explained by Kapitza by invoking a separation of timescales between the high frequency modulation and the much lower frequency pendulum motion, resulting in an effective potential with a minimum in the inverted position. We present here a study of a microscopic optical analogue of Kapitza's pendulum that operates in different regimes of both friction and driving frequency. The pendulum is realized using a microscopic particle held in a scanning optical tweezers and subject to a viscous drag force. The motion of the optical pendulum is recorded and analyzed by digital video microscopy and particle tracking to extract the trajectory and stable orientation of the particle. In these experiments we enter the regime of low driving frequency, where the period of driving is comparable to the characteristic relaxation time of the radial motion of the pendulum with finite stiffness. In this regime we find stabilization of the pendulum at angles other than the vertical (downwards) is possible for modulation amplitudes exceeding a threshold value where, unlike the truly high frequency case studied previously, both the threshold amplitude and equilibrium position are found to be functions of friction. Experimental results are complemented by an analytical theory for induced stability in the low frequency driving regime with friction.